{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "`Learn the Basics <intro.html>`_ ||\n",
    "`Quickstart <quickstart_tutorial.html>`_ || \n",
    "`Tensors <tensorqs_tutorial.html>`_ || \n",
    "`Datasets & DataLoaders <data_tutorial.html>`_ ||\n",
    "`Transforms <transforms_tutorial.html>`_ ||\n",
    "`Build Model <buildmodel_tutorial.html>`_ ||\n",
    "**Autograd** ||\n",
    "`Optimization <optimization_tutorial.html>`_ ||\n",
    "`Save & Load Model <saveloadrun_tutorial.html>`_\n",
    "\n",
    "Automatic Differentiation with ``torch.autograd``\n",
    "=======================================\n",
    "\n",
    "When training neural networks, the most frequently used algorithm is\n",
    "**back propagation**. In this algorithm, parameters (model weights) are\n",
    "adjusted according to the **gradient** of the loss function with respect\n",
    "to the given parameter.\n",
    "\n",
    "To compute those gradients, PyTorch has a built-in differentiation engine\n",
    "called ``torch.autograd``. It supports automatic computation of gradient for any\n",
    "computational graph.\n",
    "\n",
    "Consider the simplest one-layer neural network, with input ``x``,\n",
    "parameters ``w`` and ``b``, and some loss function. It can be defined in\n",
    "PyTorch in the following manner:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "自动微分 TORCH.AUTOGRAD\n",
    "在训练神经网络时，最常用的算法是 反向传播。在该算法中，参数（模型权重）根据损失函数相对于给定参数的梯度进行调整。\n",
    "为了计算这些梯度，PyTorch 有一个名为 的内置微分引擎torch.autograd。它支持任何计算图的梯度自动计算。（有点优化器的意思）\n",
    "考虑最简单的一层神经网络，具有输入x、参数w和b，以及一些损失函数。它可以通过以下方式在 PyTorch 中定义：\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([1., 1., 1., 1., 1.]) tensor([0., 0., 0.]) tensor([[ 0.2539, -0.9612,  1.1173],\n",
      "        [-1.4098, -0.7301,  0.6183],\n",
      "        [-0.0924, -0.6758, -2.0235],\n",
      "        [ 1.1078, -0.4381, -0.8923],\n",
      "        [-1.5410, -1.0904,  1.0589]], requires_grad=True) tensor([ 1.5858, -1.5226,  0.4495], requires_grad=True) tensor([-0.0956, -5.4181,  0.3281], grad_fn=<AddBackward0>)\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "x = torch.ones(5)  # input tensor\n",
    "y = torch.zeros(3)  # expected output\n",
    "w = torch.randn(5, 3, requires_grad=True)\n",
    "b = torch.randn(3, requires_grad=True)\n",
    "z = torch.matmul(x, w)+b \n",
    "print(x,y,w,b,z)#看参数的shape是否满足矩阵乘法运算\n",
    "\n",
    "loss = torch.nn.functional.binary_cross_entropy_with_logits(z, y)"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "张量、函数和计算图\n",
    "此代码定义了以下计算图：\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "在这个网络中，w和b是我们需要优化的参数。因此，我们需要能够计算关于这些变量的损失函数的梯度。为了做到这一点，我们设置了requires_grad这些张量的属性。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\"><h4>Note</h4><p>You can set the value of ``requires_grad`` when creating a\n",
    "          tensor, or later by using ``x.requires_grad_(True)`` method.</p></div>\n",
    "\n",
    "您可以requires_grad在创建张量时设置 的值，也可以稍后使用x.requires_grad_(True)方法设置。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A function that we apply to tensors to construct computational graph is\n",
    "in fact an object of class ``Function``. This object knows how to\n",
    "compute the function in the *forward* direction, and also how to compute\n",
    "its derivative during the *backward propagation* step. A reference to\n",
    "the backward propagation function is stored in ``grad_fn`` property of a\n",
    "tensor. You can find more information of ``Function`` `in the\n",
    "documentation <https://pytorch.org/docs/stable/autograd.html#function>`__.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "我们应用于张量来构建计算图的函数实际上是一个类的对象Function。\n",
    "该对象！！！知道如何在前向计算函数，以及如何在反向传播步骤中计算其导数。\n",
    "对反向传播函数的引用存储在grad_fn张量的属性中。您可以Function 在文档中找到更多信息。\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient function for z = <AddBackward0 object at 0x0000016E9A36D550>\n",
      "Gradient function for loss = <BinaryCrossEntropyWithLogitsBackward object at 0x0000016E9A36D048>\n"
     ]
    }
   ],
   "source": [
    "print('Gradient function for z =',z.grad_fn)\n",
    "print('Gradient function for loss =', loss.grad_fn)\n"
   ]
  },
  {
   "attachments": {
    "T%7BSQS4~709RL%5B00VGSR6G@2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing Gradients\n",
    "-------------------\n",
    "\n",
    "To optimize weights of parameters in the neural network, we need to\n",
    "compute the derivatives of our loss function with respect to parameters,\n",
    "namely, we need $\\frac{\\partial loss}{\\partial w}$ and\n",
    "$\\frac{\\partial loss}{\\partial b}$ under some fixed values of\n",
    "``x`` and ``y``. To compute those derivatives, we call\n",
    "``loss.backward()``, and then retrieve the values from ``w.grad`` and\n",
    "``b.grad``:\n",
    "\n",
    "![T%7BSQS4~709RL%5B00VGSR6G@2.png](attachment:T%7BSQS4~709RL%5B00VGSR6G@2.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid character in identifier (<ipython-input-3-b2014bed33e3>, line 2)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-3-b2014bed33e3>\"\u001b[1;36m, line \u001b[1;32m2\u001b[0m\n\u001b[1;33m    为了优化神经网络中参数的权重，我们需要计算损失函数关于参数的导数，即我们需要 \\frac{\\partial loss}{\\partial w}\u001b[0m\n\u001b[1;37m                                         ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid character in identifier\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0.1587, 0.0015, 0.1938],\n",
      "        [0.1587, 0.0015, 0.1938],\n",
      "        [0.1587, 0.0015, 0.1938],\n",
      "        [0.1587, 0.0015, 0.1938],\n",
      "        [0.1587, 0.0015, 0.1938]])\n",
      "tensor([0.1587, 0.0015, 0.1938])\n"
     ]
    }
   ],
   "source": [
    "loss.backward()\n",
    "print(w.grad)\n",
    "print(b.grad)"
   ]
  },
  {
   "attachments": {
    "%29%7DL2%7B3%60%7DC@UP2EYF9D3%5B~7O.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\"><h4>Note</h4><p>- We can only obtain the ``grad`` properties for the leaf\n",
    "    nodes of the computational graph, which have ``requires_grad`` property\n",
    "    set to ``True``. For all other nodes in our graph, gradients will not be\n",
    "    available.\n",
    "  - We can only perform gradient calculations using\n",
    "    ``backward`` once on a given graph, for performance reasons. If we need\n",
    "    to do several ``backward`` calls on the same graph, we need to pass\n",
    "    ``retain_graph=True`` to the ``backward`` call.</p></div>\n",
    "    \n",
    " ![%29%7DL2%7B3%60%7DC@UP2EYF9D3%5B~7O.png](attachment:%29%7DL2%7B3%60%7DC@UP2EYF9D3%5B~7O.png)\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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mEZZk6BjJ2bMPr3LyEb4MhLgLD5WcPf8on+rY05+477QCpfX7o3Tw1eP0wb9fS6/LY5WvXSqnZvRI5bV063cP09OlbyzkR1FLgkS/Nfarm+33y9h+xQ6MW0mMVuu0Ty/++Hhd7CSPlKoEbXUlvf3AP954kB7/7m66dY1oXkqXRH7Nh35y4D+fpke/uMR9+u8RBsmZPrn7yTrtIz9b5EroBASAABAAAkAACAABIPDqILB5cvb9Qdr/SL+p7+20+9cgK2MM6OUatAGnzXjwHJx7699qdTnd/Ni9ofCr/KbA1epaul9fGDEAWBKnqeTs++fp/o2cjPQvBFnw3TbhIcmZ/A7Y6mZ66L8P5fsOxKbqo8Pn6emfdtNdnZBRQvOja+n2R/vpOSUjL/bT/V9dS5d1olO++3b/47309OvDdMg/JO0YHT5Kt/SYUr785tV0/d/X6e5HD9PeX56nw8OjlL7fS2tuV4nVa6+nnd/sZRmY9FF6+h/yiCW9rfHtdP+J2PcwPfqFJN2rZHg8eZYOvslZ1dEX7+fv1F27n575766JzeXtkFUdon0prX50Pd3/EtlZhQUFIAAEgAAQAAJAAAgAgR8EApsnZ6lskF+7GpyalO9e/ehKuvrTq+nqj3NiNptYySlcdyJCyVKmcSn4La3OApIMqeRM3syYHwlsSUMoU01MJr7bJjxKcla/C/XuXv9dKNdXy3v04ml6+NHddPvfrqYr9QSxyPfa6+nav3+QHv4lfhNioh+AfrBON9+8nB8xDBOva+nup5I0H6ZHv7qebv36g7T7p/307MVh/APbKSX6Pbl8GkqyXE7Xf/M4PRMyWgHq++d1/U6cfu3/0dfP0vNvxjwqmRd7ae+rlNJX99PV1eV0hXzmp1dq8nntI5eo08CD5+nAJ3OVIApAAAgAASAABIAAEAACQODVRWCL5Ize3HeYDsKDCzl5UknQa6+nWx896xOXALOjgObz31OysJN2/x4M8FWSDKnkTB6rNMkZyfSfwcb/xV66+29X0mX/Yg/NR3hQcnb0PD385dV0iU71KMnw/3Rf33a0n+7y75llrC6/eT3dem83PR4lZH683H/3PD39+H5a//t1lQyv0qXRd+Zk3OhaXuN/+ef301N/EhiNOdhLH3y0v8i+0XCuq0lx8Rs6DfzNHpKwIWBoAAJAAAgAASAABIAAEPghIrBdcrYAiaPDw0RPyR3/31F69tcgkdqG8HcLZZo6maFTq0/30t6X7Tjp4IU80ueECvqaHn/f52TsZHAqlOn7ZS+ep4Po8UbDfHxz8OWyZHpMAS1AAAgAASAABIAAEAACQAAIbIrAqSVnmwqC/kAACAABIAAEgAAQAAJAAAgAgYuMAJKzi2x96A4EgAAQAAJAAAgAASAABIDAuUEAydm5MQUEAQJAAAgAASAABIAAEAACQOAiI4Dk7CJbH7oDASAABIAAEAACQAAIAAEgcG4QQHJ2bkwBQYAAEAACQAAIAAEgAASAABC4yAggObvI1ofuQAAIAAEgAASAABAAAkAACJwbBJCcnRtTQBAgAASAABAAAkAACAABIAAELjICSM4usvWhOxAAAkAACAABIAAEgAAQAALnBgEkZ+fGFBAECAABIAAEgAAQAAJAAAgAgYuMAJKzi2x96A4EgAAQAAJAAAgAASAABIDAuUEAydm5MQUEAQJAAAgAASAABIAAEAACQOAiI4Dk7CJbH7oDASAABIAAEAACQAAIAAEgcG4QQHJ2bkwBQYAAEAACQAAIAAEgAASAABC4yAggObvI1ofuQAAIAAEgAASAABAAAkAACJwbBJCcnRtTQBAgAASAABAAAkAACAABIAAELjICSM4usvWhOxAAAkAACAABIAAEgAAQAALnBgEkZ+fGFBAECAABIAAEgAAQAAJAAAgAgYuMAJKzi2x96A4EgAAQAAJAAAgAASAABIDAuUEAydm5MQUEAQJAAAgAASAABIAAEAACQOAiI4Dk7CJbH7oDASAABIAAEAACQAAIAAEgcG4QQHJ2bkwBQYAAEAACQAAIAAEgAASAABC4yAggObvI1ofuQAAIAAEgAASAABAAAkAACJwbBJCcnRtTQBAgAASAABAAAkAACAABIAAELjICSM4usvWhOxAAAkAACAABIAAEgAAQAALnBgEkZ+fGFBAECAABIAAEgAAQAAJAAAgAgYuMAJKzi2x96A4EgAAQAAJAAAgAASAABIDAuUEAydm5MQUEAQJAAAgAASAABIAAEAACQOAiI4Dk7CJbH7oDASAABIAAEAACQAAIAAEgcG4QOL3k7MVu2lmt036kKrXd2E0HUVtK6eDBTlrdCUfWEft3VmnnwYDCk3VaTdCvRH4gBcJitVql9ZNAIbbDRDsPOUi7NybwDMiebNUJ8CebD/yN8Znxp0ifoY89WY99LyKEOiBwagjkuRPO/Q15Dv19Qzon1p3m9Mbzdj+tB3FgJFeNDzPrUjh+67izn9Zza9QE7SrLRB/Wa45HJXRyhY39aNLO5N87affFUvk2mw+Tsk7tYYo41XeqeOR/Xl6qG6zPdVwr8P5n1od/QP4z4cMNlVehtJmdjUaEgZurk77Jg6d9fck+2sjwEm+yz+d9Ku/r1dyb04PbGbvNY/9LVHmW9RbJWXZASgb6P5WMCbhh4M1ONVp454xBWmnH5QAZymNlZKN38hRZZsbL5kc7Ua+/5de1b7zRGNiPg1njpZPUDgs34UOKTE/ZLuxkKzs+E/hp+SyVcrcFf09H+4NtI3/1i2XrEekh8kY0s/130vqJ+2DA2aSzfcVnLEuTCiUgsBSB8QIdxqpRPOB4vYlvRnGTxk+tD3qDGvTrZMt9ZD4uQuTFQdqlD6s6WqPRmYeJ72VsiJ+L4VGMyJyI7gSehNON1XTyORsXAww5zuyk3Sf04WhbI3Q8qniyzeM+ur8vC1ZDRKc+OA0GHbzY5w8Ho/0Ax+cb67T/yiRnKaWCa8Z5Cx9O0/sjhvA8+E9gy22q2MY0rxb4o/e9cI6Gfj8xF7cROhjDsiyOO44AzXU3tost1MfEHx37o3gcz23CkGStcYBFGcUSTaNhuBx3Pb6USQe/X3K6Z1/Ie9IaH8IPLLLeVRcdMz0P8oup2B76TSD/MWhUOZ35o9stkzPZyJNBo7IEKGpz4FUpxkGLDW+csA6qBXbcO+u0jk7PyCje2G0kf4rVQNIOXjupwlx77pqdVbBQw0+jOKFfN6E9/8hhlzqlssksn8K363dC/KtaI3oi66i9+m2lxAUtry5TI92vRhsu4jP0OeFBPt8CnNTiCgQ2RSD7Yr9wyMJLi7iPo+0+xzS/6V52L/7r4mJN7nJc95uolHy9mwtl/uzTUxNz8Sha3OfGSLufoxwfbNz2815s0/BL/eZC6G8UdzImbS0STuUayNZ6NDxZLqOXsg3T0Elxo5A3QGJPVb+0WGjP2kuwmYx9TR9hz3qFcTr3Xc7XzhPtm9bWC+aF2LcIyfNQ6pbgIX1p/JL+FbumQ5P/JfuPGOpYV9Kh+GCNIRHB3j+oV+/7o7HH8POAZPbNZpNNfLHOd7K/zFtdLvyMb7Kv0IcuB+qJszLPaR8cPDXFMmp/03qURLiNU3bQ/Wp5rj13HM/ZSqgrhDZk+fq4bJNTyTOsbYd6Bxh3wnBF9rVqp7jTsHbIfzgibtg6OVvzp2O7nJzt8mOIa5WoCWgF3ABoFmcA1hLlOChy4FqnfXbcuYmiDF0cM4OvFrIQo7n2PIhlDheSkOjxKge4EVEzoRdw2Vbuhv8c7tOPS27Lv6oWYNH8h2xnJy6PY39R/lCJWfwqlsVfaiBV/WtxkQ8SVoE8hcg/vv1netl/n937Wbp589308G8vX5YzxeKze+de7+prpuDik/LtNg9owMTiWvy7LdSGweDG8WUa5Nt5Yetp+XonT5nHnJyNNhSyGaP20t+dXw9kLdXBmDrHqUvQrgkaPIO+rX2DuBPQqTypLVxTMvZ688DxWHAjW0iZiTmshUG1mVTka9PD1nd3A9kNpjLI82Ld5teObtMrm1mh212dX3btVJH7eNoaTx7GMo/XibnxjKOS19iIGAzwC0UeVU7RYIwj+U/If0YybVBvMPI+Yuj4+JEbeXyQwHrbTK27hs2WN2xbZetFZLTt2FZtPpAvyjzKOo7tyLre2E2LPtjSMhaeOVYPYkRVZK49dxzLWgl1BeMDtZX4RTrXDlzgsRLrJuYrd9Z4WzLmjnDv1y/TZdEpb++D0/s/xyFtnZzlb4RlAHdf0BLpwJwDykui7g3gqp6LRPfGLj+6Qg5MfTsglxih9pkL5nPtWUCWeYEzeXW2ui+Tyho/O7JM6EV02UbTydOIzlI+k/2Owb/KVe1Ya+qJwdCPGL8y8QMsZZEW2enafWLT2OVSIIfvMrlBTumlJ2aUDH31h3fTzZs/S7/9DMlZmBz+7ZP0zk1KYKO/e+mzU0ywe3+imhaf2N/V4qv9X5c9HT+O22fjd+Pb+rfkzMamtulosdot9ovmj5J80/401I8p8afK5NsVOyoaDIO+0i5XNzzz32SNIB4z/Tk2LdqcBjGM9e8/LFoU7yI8i8ISN43+A17SJxyzxYeNej4I7anriC+PWTgHRmuDn1cdrs6HfP8st5tnU8r4ttP2H89v43un26SPULzoN80xZl4QF2t883HvGedetlmy2v66XAayv9DcluRDzwfqf2eXHwem+LV/p5/HwzikBGt95jCaa89Emd5MzJI5OlojZuvrGpd9QvZr+lFIpWIrBhi3Ri2/xdz34fuJ2NAw9SOXYSijtkzO2mJrgVwnPkUbLBY7D/7//Gx5aa+gijTlyk5ZDeAa2Sn366cK8riMlWMgX0jTBQjHThypLuBde67ITrmTduh7BCGfwcBtqr2T0X2ZEJOLjeGVHXtb3GrgGNha043tfDz+VRWPRd1EUeDaSes708k7221gr+VYbvKISh9ERZcwGTjFzf6rx+/z9FtOik4hCdrm5GybMcewp/jJku9mUDzITzTIdzlGfpfnYRffJhafLEeOm3qe50+nB/TCxxpdnOZ5GNFV/bq5SvxGulXEwkKO2WpTFcQSPdAsukHf3L4k7tjYx/GR8VZ6TsXVaLOmBQ3KRnZpr5thK4+1qZbJ4RxgQKTDuFl5CXN7DceMaJWhYr+xvFr2+FN4zZfKi2hV/Btui21Yx7YPC/g7klP2Nm1kg8aX5F3MW+goGbT+1iL2LvQf22XzO/IfnXAtmAM+Ti33Aee7m0sbj1ggc/UphTsT0/NHlwun3jY5NpK9Se+dB/m7mozJceRgfuRTUxjNtWehsz022wfzmC6uk65T8rQ9F/s/sWcM4nnO0gUYZ6nL//yit/H3X03fysvORUqkWR+5ypzj/fkyDIXPlsmZAEDMovI8UL3jiUiyOAtdqc/X7JTtyNe2bnMn/KYDsw8KnpM4JZ0i0psPT/UY3TsZ3avkrAaD6hhFtzoBRMb5TwjiiTNYgD0ow8X1+PwrK49FTc7K2z55ErlJrsbIRKr0isxDDBWmcz6haS4p/8OcytxLn9X79pihnGzlkxubpOi2d/7weXp4+2fp5r3P+UQut6n+TLvRzY8zymmQ6qdO05jnvc/r6drN25+krzjZ+DrzktOkwlOSPy2X0JC22WvFoMimaGuZ3/nD16neG51FJ38aKIketd9Ln22TaIVjNF3Ct93TaeScHf7x7RjLoQ+Vhdn7Y/Vtjg8qCVGEeENa44JqqIuPqjPFPIeJp43lebHyssiHaK1eFiq5GuIb3CwZn2WqizhRL5iZzaGKC5EAFU9qDPqa9pm4I/QtdlJbrmy3eB2Unmw/FZMm45bfHEYyDmN2gHOAAckV6jTgpfUw9ikNIS0ZpPro0wXbXNYar7saG/G1NAZ3bB9aQ+krHau0vqO+QyTrUDS3hJzDj/2n69/mmQzT10l8Ttt/tCAbl/OcNPNv0kdy/xY/MsMYMy9M4Lu+y1b3TYc5H+J56n1Q20o/9xEAACAASURBVJ/LO+0lPnf0AYQI1zAgevRSMtprekyk92bXpss4hrh9VMCA7cFJXpl3kwlfJhDbMNCNMKoYNnkr9uw/E/FS4+1lp7FMu8hNZeq/QH5PivWpcvrW5fdbJGeaOAE0AIMVGzvOOKgQTcq8Y0fITukWADbKdHLVjFrkd8ZgB1fGawAHTqIhKOXslA2LfL/dI4MBeVul5OQGxjrztrhm2avzcufmfCLjeDL6pK6JQXxmx5VNw2nwr5IUP+tk0ZND4UPjWO+yCFq8KlUu1Db2r7E/dry33CzVRIU3/ffSb/8gyU95xLDUy6NzvNGXBKkkMZSkEJ2aEJlERSVdLjnzvIVHrf/2nzn5uXcvPSw8pI2Topo05eRC5PhHl8Dk9mWPTTpaRUc7tvQhufSjmNxX6evkyImctEsCVZLVwqd/dFH6a3u0BFfw4GvB97f3PjGPOs4lZ1NYWu/Md3kOx77JbTIPeA64fmXu8PxcEkP1p9xKmDpP8qzhjepoTvQbiRzvl78qXTGu/Jxe0qXGhtx+wI/f50aOX+qxIK6l/t3mWIgFjzVG81zwpmHM360Jjr7FrvGq8ozW19J1crwiZ3xB6sO4NlrvAjtVfJeuBQM7jRK6iXpRga+hHqUHyzjNN/vquE/8ODrhVE4IyOYyf5T99Tpj5JUb5295LsdY9vMmE5m0v/M/Yauvk+NVx9B/VPumxUyvPZbH46fs2J28b8rxpPvTfMj7O8JwFO9MvfINlqabPy1WxO3yYXr2PTkIqL7R0evlsnuxHKNyXZvf2tbNP1r7FJLZh5se+X56Hyx9GlZ5LjbeEktX/AJA+hIVj1Ffb2KZ2H8a705ON99qO42rcbntjxtNwnFEN/tBlV1OzORa14jR+CpFV9giOXPCVOZWAQG8c4YiggFei1UApkdyRmOpuxk/YxSWxU0MHk8AKt5i8Gp8N0Z17YpZX2+AglU1fDdsu4pwEmbeBpfgTZm6PcLFC6Qx0W2ajq73Zd9P3x+Hf+UTTLierp1wWieSp06s4ssS7LSsulx5q0LP0/ko981yCH01nIt1c8+JhD/pcYkKnVipZKXb9MsJzEknZ3TKpB/NK0mIfoGIkcUlRVVHTWNYzklTS8b8PSVJGZd2ijf4rpzC6h/fZjo1gST+28g5NabwMzxq0qww1PjpcsFEY2n9ZSIOl3jjfVL7vZxkke+HcXYmpubxLebIHFo/yXKRj9s50+pZj7ogKj1urPPr5c2a0s9P+0EbjVcba5a7jBnGb5qHJLubj0Es0ZgbPIO+pp0HjuOO0LUYSW25cpz3a4rtQ+MF+9mrxyO0sbOTsAv70gmkfnscdXaYmvFiJ2XzOVsH7ZG/Wt8WpplP37/YpdDu22W8XJ2PUXWxPz+SWHBlGQJ5O7uIHQIfEo5Lry/Vf5YK2fUj/IP5xz4mPuIHWb/cyO+dTUbrr+c4vrc+PmmDQoTlFbuX/es2pzJWJiuH+KTe0+r+vZx5vPd/LWs/RlPsy3kO+JhV5rvaBzMPbRfVJlQlnsq80naT79gZ+UYxSggG841pG94ZE7vGtORw6sM7YXNS1y2SM82aQPeGoPbiNA90RqrHuYX7xW7aLa8CrY5BQBvQpsePftOlBkY1MUbPpmpDi2NYruO77EBjLDpjj0nNtnSy1UXcTdYgOdPEOzq6sZS5T2AHjVUwrFZN9TsO/8pgNOG0vamzmrhjvnYRNrJXjCtnU2CaOthMlHWQ0URq4sKbfrWB5416SULk0UF1DR+Xk6TlpJOzekJWkqCShEydMuUEoz1eKI9aVn2HyZlLSIPkRZIznwQR7fqYo8Pq7JKz/lRNJ1usv9ZpBsvqK+zLgwREzYfOz9UcIN9elWTIL87MR/WtfE2hxX4zT/Qn3EqWRrNsvog+xxU75wwL+YTUz2XTicarBCWIVaa7uXHx0str+gYnZ45XhzeNVzhG7RY7x3Am5lDvyfGKXMTbn+xx9xFPpYciy/zt2jZtTz22lZ0dWsNi/WTP0WQpfjHpOxY/nhPalwZl+e48zRseE/FgHPvvn5MdZL5Vm0jfAT/Zw8g4Bc80PiNbKgLH8h9FZ7uiszv7mJrLAR7R2ul1qLhuJ9TGozz/iMDQT6LOi+scfgv8yPgQ9XcxTOaR4LxENy0uYz+RE7T52UbxmE4OiZ3kD6OE3c5fHWsbdVUy+mbsRvpHchIltuNqnf7PJh+KeT+O4oUSU4qnk5zVQE4AxMBWoxeHYmfgca0/9REnEYHlWsdTReUnrfbqJ6sZK10dbz/G38swuXJ76JTS4+SuY1n8wpgd0ExIJUaWeToY8sJQJ05xaO9sS++dU27OXwkvRTPhcuUYn7l2i5/3E7ofTdqIpx/vA5+oINearEwkZ1ESQuO6Tf+ZJmd9ElJ18YlXSUDaadjgpKuOs0lpP84lcDLOn2oZvjMnZzNJUtXN8xDedGUaPS6dnXQ/Xda0Sln8RK7D+VPma++Txb//WxKjifgwE1P9yVmLMXlTnOO20KefXKE4oz68Ivosp51zpBvL7XWgee7iR8ahHy/4+Kumm9uyfHWNCWKJpmHwDPqadj2wlKP2PkaogcRDY6aapMgx6Tjx12Aq9go+ex/6Qx5TbbNAZpG9Xcc2nMSnESilIgs9bkiYGN26zlyxjH4v38GT/NQN4+/5lL0EvYzKb/40P10mYUJa5QNWT0e08TSknq8LbME8t/Qfw2urGzf/Cm7xI85kg2A/GIzheTbQqc71reSNBy3G0PuJ2HYgqyTlcu1ld/gFMUlLbH3FjZWOzmfsGJcMyRh1zdirOK/aRkUeU/eY0ivbm3TXevu+Rr5hjCo0Kz4lTnT2oH5TbSLbxDXwx4nek02bJ2dsvNGGPidW7KxFcQYzAIH7sFPaZMwEVOcoWpPeKCOZSr3IENIsjiB9ZIMwca9lofI2Tqlx8vSm7mmcdtjat9MtO1rbONWeXBjZRvfyk0G3Hbd8IvxJZzex5+gOcXeTu/kY4UgBJ/uJxbMFEQmii65OZsLSbvr9yVmQgNFmfvCdMzkdqqdULpHISUKfPOTH+3reJJv9PpQkVSV5UidqRFuSSOaj2vSjmFXfIBHJbZREBTKa/guTM9a/PSpqv3Mm2M7xEp3L1WFq9BklWm6MtcM0ln6+hX6u5kPXvkl8cHPB816WnMkHZ0G8Ivo8B2j+tDVAHreU+NZ0yLFM6ps8fnxr8aV+3juaCjs/lu6bLO2xNp3GmPaAQM/fbXb4bWGKYmevgGipGvIe6uTXhnzvY2nlOKRDPcpY2WSqdbOOnyiw7EE8pCEtBk8QKE1MR2Rwm7rRaE8/lmXsY51N2WbZ33ta2t/yutH5cxm/80A+0NBzo9fCyH+m/qMe9TLzt5dxXKPxGPeaahGb6zWZ6xb7YJZBj5/iF7UZG0Qdhon3oPPiaodf8Z2p/Yfo2ftmi9XSh8Twuvl7L2q2x/GSM+LBOsj3tlRs4DZlWyPP3Jo1GcNEk4ypyUOkyV+Z30zeoeIR6dTNd09T3W+enJVAvJZHFovC+Qfw6BfMd9OOmaxRECoAqE8FR0b1xhDZNzGKnqxmHBETgJXBqVqPoftunAhSriP5XTd1G+GimofF0UIRBZmorhH2OraWVprtUwKCdrqMxeC7LI10h7FqqsWl/LuA5OxZCYYJVmllXVpgYZvfWfOnsFW/4i86gDXatjTnM7Z3qt8h848ISqJDm/+8mW+PCP72D5+nz+QHo0sCkse/m95Rb2uksfoxv3fu3UvvqMRHtzX+OVnxPIV++55ZSSrq44P0co7P+U2OX/2tvDWytv2sJm4mmTEJV0uCQrlKshe2qe/EmfZ7n5Q3SkoCZmV+5zb9vpu0Nf6TMrpEK/fNp3INw2IrlaBqubwd5DHNNr5h6f0lnBtqAcrt+U1yeX74jd5EfJhb6Hge5blCfi7zT3/nrD42x/PK8Sb6NTkri9aLg/xDqmoxNjqyTI6OfozSA2TuI11zXZ3bCjsztNwYWVinprfoP17Uc7z3cSPHiPL6Zr94M48Wj7RMGvPK220EhvUUGzXtEtOGidmizWXGMvOMZdby13LhXW1QG3JhNoaK7KS78hsa3TAayxPRZzurvUn+wMD7XZMv21z0b/2Yjv8eZZExt+2a77zXvQh9D/TGOv8sz+g7oQWnLP9L8B+ed0XXmXlTRA0ubv4FPSarajzIc0tOmc08nSQg+79ms7nuUXvkQ77fkj5+zPy9w2/GDk0GN44YcTzo92xtDHUKxjkh+7njOgS31V4yl83eLfPUc0zHCiMfjx/PddbRxYheHM2vbzU1np/D38i2ADtDO6UtfoSaBGIFxVByJdLxApQNrycAjWn32aDt3goZg2UU9yBZAjlIG4OXDuyQA75MUy++E0aXZM4EdCeEv52R2Xev984BpD6eFBk7vyEwYwJcCFu9sOvJkMdKMOwXRKFN10YnxrhOSj3IjMty9PzVgAAPS1fJKpsXNUEzbk3fxqv4nfmgofAtviGvstVYbVR22E8mAoPkZTymP4UZ912YjGwswzHp6pNB4T06kZL2H/BVeT0Xve9W39MbQOdjlobEB/mUvs2DSkvmTL3mudzmtv80UM83FTM51krfvg/T48fRbKywczl/aObj2RCHKrPopeTJCNpXUQexROPFMgqeQV8rq9ax8FdxJ9OVGDN4BI8x8zJriaQsdlSnbtIUyGk2WSWWeUxls9b8wNpFyAst7lew8fZoMbWN4pKssYKpa6ZbwryTTZ/UdZgGRMq+RHRp9CZwM2TIlrH+4hPZf22yxTiE8mW+hIvBKuzr+pgE/mX5D1umYRL6mAFwcDPAoZu3Mn/LlfylrsGNtMFygkazf3wC3iguK836KMti/WeprOKz7arpNPxY0kk75L5G96JelmUQZzgGKfwHPipITdKSTny18XEYI8oYnl+Mo5XTYM8+Yds1S5ZtRv4azyZiUqXp+Tn8jWxnkZxZhlVMLjCAA6WGbWz8MaCZQwlCiraRw4O06QbfqrHV3XKnLBo92Fn0TLwXhvTuHTk7el8/npCe7uL7Mll7XhMUgkA60fucNBGmc355sqKebPL0KiRn9vSqnRaVxw/5ZMo9YhmeVh0zCXxFEjrvbRxzVEzkdrVAhO2GyGnFh9G8yXEq2iAYsUq8kA3JRrHGEJq7yfpX+gq7PNJuIKa+mD7HKWxnPfVmy/WaWxtLLJ6Uq9PJ8djyltfzsgGu+IW0PIaSbC3zBbPOh/S3q2zyj/Avew7Z5A82dUzHz8Ei0rLN4Hby86iX7D95z0Mb9xGGc7q5+TfXvbZvO64SqIXT8q/K4FQLDodurjsf3tpOy5XIPjGK/8vpLO1p7MfzQfP2+kd7Z8+pjBnMadPb83P4Z9naqfam82SLxxqNeLgBAkDghBC4eMnZXFIVJ2/9S0Hm6Pww2k/IzUAGCAABIAAEgAAQOMcIIDk7x8aBaEAACAABIAAEgAAQAAJAAAhcHASQnF0cW0NTIAAEgAAQAAJAAAgAASAABM4xAkjOzrFxIBoQAAJAAAgAASAABIAAEAACFwcBJGcXx9bQFAgAASAABIAAEAACQAAIAIFzjACSs3NsHIgGBIAAEAACQAAIAAEgAASAwMVBAMnZxbE1NAUCQAAIAAEgAASAABAAAkDgHCOA5OwcGweiAQEgAASAABAAAkAACAABIHBxEHgpydn+nYkfLeQf1tQ/JHdxjAFNgQAQAAJAAAgAASAABIAAELi4CLyU5Ix/RXz4C9zuV89HtgmSOPpF7vUTN4B+xfvGbjpw1SlZPuaXxkvfqK4js3VF5r/zoJesJ7mf1v7X3f2vk/eDzrxm2q6xOPkX5VdptVolxkLpNUeP29m2hM/yhJ7GeT+Z5BX4WkrEM/C34lfL7BpjsqhW4aT7W5+1Pq77bVQe8MpzaOaDluE830iCU+k8afMFHC3WMiCYq9LkrvF43WlT+y3nrbm8tDLNqzA2F4mGfqclDjBaMm6mD9lm5WOuZntC5aEPngg2JyDknBwnwOJYJNiOef3IvqT8YcbGidtz/CJ7+zXhWHItGDy0/dxYkvs4cfXJOq+1c3zcHmm2+4YdeI55PeZsRjxG+ne+uiAe0hgvw4Z62O5jnpvZm+iUPZFlkNIC+4XYOjrjPhO8HY3j32ZetP9blT0cyZX3T2MsM988luYtYXvqe66hshRzBvugzieHRLqGzZMznjwlGDKgy8st+M2AvmTCUB+/IWfZNEg5UFMg61Ig17c5hGCkgrxUnei1YPBkN+1EOJpNS4DXMYx+fDVInj4ZioOP68t2Uz5j9CyBt9A+eLGfdm+0SWvlLraV5Fb7g+dB+Co+BxTc3MbLyk4yq8Va0y5CcH9Fs8kW2Ko1JvlQIAcjhUPkA6ZO+7XFSZO3fhz7MAdlQ9vJQYsV6Sz68Vzp7U26HDygeehkI4FKnFg/OOjnHrVHNhrJJHJoRTcZr22paFib5wA/tkuvo8WaCDufVLyiYj/e94rt53vp+2zbyFa6V0qzPtDZQulfbDvGyvkT0RrZMKoXUYd+Jx3oGmDUjaM+Sn4a9WBnuCmrbeRjsxu3zWxOEmu7V15OJl2vta1lo2OOV3P2yOtvlrfrO9JTx4HK/JiF4dwtfhu2i/28rlIvMil/eHGQ9snOU/O/+p+O+Z4H+bPjE8oY+H2ZR23vI3L2Psg27+ad0NT8rc9Nj5PxOiZoXZs8fUlhqRu3mf8hflomYjDwTcZE6f9iP61vqPVZZOt8lfRU46SfXIsek/NC2WPp5p9ja/Urpddojok86so0Bv3z/iXQf+F47jby3xu7dc50MWIKS8V7utjb2M+NGh9fHCTSleQIsec28SE9J3oeNQZs5bsyh8SXer/iOWhsXlDofHIaHd26eXKmR5eyX0gquEFfqarKjJxETQpxEmNEYxihagPelByVfxna9+0N0LicQMkbzd8bFr0sHnPpzvUBduHmSAZtcc18ZGJkAr1MJPcqre7spoMXPRPu7x3abDryGLJNt0nifjJZRvwLzwBbL7+VPctd/a3ztTz5bbtM4NHVYtWjEdWoIOMDtcZpccDRMgQ6aFtozDSvQMzejhm/MKDKeE1f6qLrqN+ovqPh9FTt1uYldmgMpG/ga9RkY4ayVTT/6gaxzIlBH4l14VX5AM+JTWn48eo+q0qy2TnF9QP9BZ56XdKP+4zmyFy9+K+2qS4XSZiH7VtjEPlNgJuZy9UHAtpVWSnQBiJ/wFZpSNPw2uiKD8o1D2ntQxJGRxevukGani7njmF8FRqL55kMWHCNaGp9uvZN/LLXL38QJP4g8uV+JkZpGaQbXwP+nYxmgLoJ5Cmt1uYbxh+WNZirijMVJU50vknyBx+w2uED2Yc42dHtzuNHdEX2ZgfGo8ZJNZrW/zonS32kf2cTz7fRHD/5ovvMl0XmKKbM1pX4uxWNW7/oPzBQ4s7OabZ9w74OVbbNvuPnTe15AgWyT59kEt9+Xoq/NLa9jiN7D/y4kRqWOlm4Z8RnwKPzySGrrmGr5GwbZzJgVwU3N3zI+8Zu2uXHUKYWd21cccrdnDx0i/U67XPwcvS6zUyH5+IKb3R/L58i5aAqzpCdOZ70GUvGxwWyqG6xoBMdsy2aDfleMOJJ7iaZoxXLRTo2mm5Ive15TYwJJ4idTIaef2SRfUHRD+mRaOJX3TltlXtpgeVhv9R+q0arIKpqw4ShW5h5gNXfnJRRu9bR8MrjYh9088XNKyOHpq8V8OVRv1G9H+9PVopfdvJPfmJIehU7KL5tzuZ5ufNgP/gQouDl5iSJ2cZ3QpcKZyPVbX6s6hwUaXz3gQf7feBvjFlQ7+ku7SfjFJZSZa7G73SLxsX74zrt13FiFz8fqT7QJ5JnqU40dkHc0lpQ2cad0so8o7kkurm2O+twk9N49XjpuZh9Ybc8peBomzkcYNaYLC8NcS4xtmsf2GtgG9JH6xcKVn2EWjU+Ue+AfydjNC6gPbLt0vij2HQxwPhg9v0uqanjm85sf2PnkQ8U+xTcd2qCRUQzP4t75rHzgPZZzXfI52U/yP5PsVHsUWjvlg9z8zqo1t4qf46fxC/3Gcnc6oVnfarDfwVG0T67YrPDMp6tf2d/RYBtKnsxVa8f5c3V1m6EpbHhYj/XTJaWLW8ZRTJUW0lld6WxzaemsJif3x3xWhHTtbxrZzP/Su0x8Ns+OVObDZ4cyhG8Qv6+KrOgQGP7TYRMyHjSzhqjBEjthF5Gc38MgGMVs1M2B8wTrm0YyenaJMyBrzlidy+BTRZ7ZRviz/ZxdbFcm9dqnLQf6PpG1evZAmfTfaKu6uDwU/o3Xqq0wH5a9m6hMZPOTUxN2y0sSoLlxeKbjIeaU5UAy+IxavPA4q59qFDQ9IcL8k7apccVBe8pfEdto3pRROMmddF11G9U39EIMOA+yheLnsN5wrq0+Se+krHOj95yLOF+LV5xv9EjGepT7Tnf13FK1LN2ltpI16Kn8yUa38dV59tC1ukv1d11aT8ZGPry2LdlmI3vgc5iB7V4501JmSeB72Tb74SPmO/c6R+DbrK0Uoxpa+dSlc3rWe7v7OfTDm0vHtPmeKMjdTkeLvOjHq9JuQOsnEab3w7tPrJP80uZU3O6xu1tDrPOEt/OMjmraJV5STF4w/hTSbjCAT0GVh7jJP2juOGGzNz2vsIDxB/lSpVs03Va68SY2wnzZj9ZW5t9sk3IHlVeprWTdoZfaRiI3fmq5itjSKfmB1kemUfSZ4Mr6ziey0SJbSLz2cuoMVzCdmH/yTnNfJbFDLFTtc0SGaf6sG0HeA33I62/yJH9vNmN9G37aS9A78d6noiOchUeRCWmG/kV9fa+5T7k9mLN3J95csZOU4xQQWCDNaCbzNmBar/akMEef1LZG6MOlcnigpc1QnHc0YTSxLYoi2NUZ6IJVxcKMbzWQeoKM4+XmvBMu9LK/aO6LcSeHcJ8BLPZ3qOkMXBwT6tMcIPf1KfWFR/xmzzZtV9Z2Z3fKbzDfg8G3xucksnrxPfF7/SmMuzXfzjBck0GNz+/Ap/SflMxk++P+fFFsNFiMaoXfYoNJSBOXrVcenxUL+31qudRrUzpyW5a38nfO+KYRN9LVRubXh69oGc6NmYIbbHh1GIxNV7o0HUgu1o0RHYZ5e9HnxJzv0l/aQtixqLXX3jWK9t8QT8ZoH1M6vR16EMaF10ug6Nxag6L3eTKdp/zpVndxO7L9afva7IPkh2EP/NR96RShJPRMfPW8cwko8aPMl6df1PcNjQLlhFvbaNtyhFNzbtrd7FKePKYHm+yZ10bpK+5FlsJ5gYf07HcBPw7GaNxVBf4J1WfQPypHBkHP1/9fcFJ96360ya0x3Eou7KVxBuZS9mHMi2eV7wfCPAruIR2GshY9R0VOptEfPXgMhc22LPo0VRuOuoWbXNd7jf7ZrzW28TmZpuD//3/qceyFc6mv7d9u28xYg4b0cfKL7UncyUZVFIuRMmOkzYpdlP7q+p/QsNcex0Yd+X/uXvfL6a7FLuRfxjhhjfbJ2cLnUEWATsJexAYLGconvgdgLJZFIcrjksGnZKp0snA0qcyzVHdpKEXRtCnpcVBzAQaQrm0ITskySqYEH0ptwVSY2Sdwcuj77lcdc0yRXVLpY36sV2msA7aqn6KYCyX1rt0NpO1x69hpojrYhe0ex4aQ/l0r/oH+1ZOTrzuTa8sVx2jFjAtynTZ0Rh2zvLrDydiLAuBQJauf4eRYh6Mr62jtlG9DJziJ33oOuo3qtdjudzbmu0ryVjdPKzTLiVnbu4wCdalLZDCQgI3Y1l93iaxHc4yWCVYqsoVI9lzF+Etn1jvl5EdP8JJLWLCgP24WwBtnJG+esOV+Uns3fRqsVlGy41hoTQuuUyPWOX4v5N2+TtgdlzDpelYMQxOMdu8JoaaX0XFFgrO7EMdrrZrxjPHf5ZLfFEebbtBJ3hNfuljqJj5FcQN065H9ro0XyhYykuWaNjieaZ5zJQjmlrerr3ZzFAezMseLxrf8GR9ab7Wud5jYvhEj/t2MtoR7S6ivZ/WYvNN4w/rXOadyK+xY8YeL3/v7XrAyVnDQ6SPZJf9l+BJtEkeuZcPXfMpdF4Pe/5tPgovoUu0JNZm/nleF/paf8WTqXQ26fkqbjmxKhhWn6hxPI5tdX1nQgvwMbbx8mTshGbvt72d6AVpI0y1bm1O61pdzrwn98wKC5FRUzh+2epf6XV2JJzFJ+SDaetzpK+N2ZVaGL9D/wvifEzX21HzsuXQprbL8G775EwCA5EmMP1EUSx7BQdOzXQKyFxuBlHkeFLlxViewW+BIfcb0C+fdNB3Q8TJGTzlhHWB5zcC5Vfw9/JraTYrZ2Pl5/uzM1lDN6fROug+uV47opavjW9yRXWt9fRLWj7NjeUy2Gd7m/7FJ+Stf6ILfcewYmACoOZQykRD++tgErZPa1zQYBmsj4kc8m0Wfz+bMAZidklh2KcsYryBywsIBc4eS7+4KPnLAmcCboeRYj6F76htVC9kp/hJH7qO+rFNvI7j+6YrzZ/sZ4yZ2kh3NhQ5WJc+Fhk/lb7uOqQZJASjhbLJ3og33s5XnazUr/m1Hd/X6zjT+prkTFV3Rce7a/cV3rb+fuhDOQZqvGosYB59e93wMU3nJ+U7y4Iz2YzpUV+OG5metHs1JHnLeA4wlEFOR+2DZKvMQ9s087b6yUY2f6CQv9PjdDJxVdrIh3tdjI84+YbzT/TZ5ko8QvlKjPIyRMkR8Q1syTiZ8RnL+kIYHuMe2w7WA6tWYNOhDoK1vTbfIfxPIP5oHQMcenxd/NLjWdneL8Svm+wFFebX1hP2n2B9bWuuw4+xa+Nl3ZvbQ9Y5TGJUGsW+oT9ZG2j6PO/UB+TW3nKXaXf6S/MU7mVd0fO7m0tVByIY4e8ODQzuDlORqVzNnHZt+XZ6fBsSy9Xaj1MKbEe4GT0z/9UN2usTr2ITflqp+RDp28XIKlqv9aOwegAAIABJREFUA9vF+Cx17vvFdDfDbixXFTAsbJWcWUpZoc0E6EGoNJXDxzQLMPwK72wcAtpOoDH9/Ts0prVbI2ldqCyLmQtsVdjNC/nxgcbHTN4iV9a7yZgdssjA+Gh5rKNYfbJ8Ud3mkm8/Qjs4Bw0dSLsJ0o6CWe7uNDXrrmnayRzIuWAhMvQkAMgXhk0QlU1BCwwyqfsFUS8Oun8gI1eVwCN8B91I1nUNTtlP+fGoAEsmEQS7eG5phtn/qk56sdH226isMOhsonmr8qjfqF4NzUU9j7LtKNGnf3buzSW4es7J5mBqQSjcR6dxxzo50zrlcrOn9iFdzvLI/9bfa635krXUnlpyVhmUwhKbyvqgkmpPZum9xoDnVJl35BeMJ/HiOaXxDqiT3PXT/t6vghF1I9AnyLk3yTNO9rJdaW5mu9O9808z57UEvS6NF/Vz7UtsoskvKUc0tbxdu9KPsdZx1elN/IUWXwXHIpj8RpTh4XTudFD8pc2Ml8ro6mi/2E0nFn8k3ou+lb2X198PPvRibFWM9r4g9DU/Lufvh7U9GPEjGwkty5/9Ta8bRY+uXveptIoQnawSk4Un9bN8RfzMJ8vc4qa06mvWo+ml20bzXNtbl12iJR/OSRzTmFY2Vn47T21bHVIKtq9vpfusW13fDdZ6fuXyCIOI8mQd62np97RFtyKj+DkRpvFdAtdja2WwdqC2eE/c9yMcex8R+SyX/m5pv34k1WyYnGXhlxq061dB7kGo4vGkE+PpiZZ71A1VNDkrkQn63Ke1WyPlejEGGYY3wVXuyuCYBeFDJ3ikY77PeMli02TsgkxxcJaTcFDyWX2ymFHdsRQIJlhnazfZBVPNdyhXpS9Y6FG5bCYN9+99pY5yGHUbkG6jnINCDRrG18qE4w8Hsp9GutUNQhViScHxjYaQrmRvpzNj6TC3NpnAR/h0OEnDxHU0xsnXUWBMZZ7PXJV/d3RKoLU2oLmzQN+I2KK6bCfCl/jyQjiJvehn/dn4cMhXxwDdwdbbeZTbGA/jt/146x8i4+hqZdfUapltPtOP+4x4zNTP+EGVY2FB4+9tyPiRrMzT4m3J5zabZE3M40m/V9gV23WP2opNzfwqMUn/XIlp1xL3urDuskn084n4nTDu9gSB5HFzteMZ6EcqsY4Ks6pmsUlNXmtDKxgePSatI5UG/Esnmn9nG39ccsU4zMwdn7wb/Zu25At13VuQnHHsId8heiWBEn+S6xx+wp36WxxLS+TLip8e389D5x+VVrZ5yE8I+g9paz0VBj6j5aq8qL/3IbpvWA/X7zr3ovFONyVfw15VmqKnZxrVzUBP1WP7osVA02H5aU1VcUm3+/3V0Hd4UK+DXTOFct8vphthlx9VFkp0jXnoHtPlDZMzR0w7omvKzjZynh4EGi4GyRMm99GfSOY+habmzeW54KQN3fhbAHN9nbAl6NV7p+P2t45PIcT6V2dsMvYTm5Eon07ZgGb1yYSjuu1l33xk7OAj580TljaObZHo+xqaJggG8pF/1CBH7Q1b+lJ+/6iPCxqRr1U7KX7cr/hnlYlouc2HGmKLjq9tzHdP1hmXSj/qRHRGc4/6Z/032pxH+koAitom5XObi0gFqetsJw3lypjbOUD60Qm1jx11JMum4ojagOvFgOdNp1u2EfUzPsiY9ph3c6/IuxH2NfETP3L2ZZrSVuJo9Na/CsDIzxxd6a/xkrrourRfMJaxpO+N3Vintd+sB/3zZnBBzCfszNxvxIhntoN9yxzZjGM+6aN8Q8cjocL2jeb3lN8yTja+2YSFqLc5GvE1mxOmN/j5l+o7wq/FPtGBcej8vLRO6SEENr16mnP33ca2MBz4W7Wr1sn3NTx7TKxKg3lBnYhOlwSeZvwpkmn5xf5VaC+vv18af2mc+E0l3k4mTfJSMLyj1tqKecBf+TfhRz7OMUB/31FYdvoJ7i3m5T2SlzXiK0SzvNN7u4H+RIJlkvjhrsXvzPqh7UXjzf2c//n+RGBKt7YGiLb9Neu2dB0KY1BPdMOaGN8cU33cdn2dTwx9hyXq8a08VHwULLSuMV2LfbgGKP+Y9rExZNsnZ4q5TC5hk4Njv1GRdll4BIQGlB+TQfX0mQ4HRT05G3VPX7fkcjMW866Ld66vYDIPndRZSqynXgBs88Sd40M9GU+tf5Mxnoi5nR2qyt8nMUTa6tjE2l7+RmNJKXbwXq7sNxlvL7OX1dB0E7WTyQRCai3480sE5AUCGnsXCCZ9TbjlMdV3lEysyyI/cXyFdHT19IMgI8GmXUfzpTDocIoY67oJeZV8ekQtL+U11Y/t4hfkyiH7fbC5ML7j6Gs/k35cV+aYtqW0V46ss/aj3sdr3+MUPLZ873GYsA3jZuXM4tCYoD7QKxR/aT89WMtebTEhux67Tbn4jMwJma9sYzWHuJ5km0rOCi1Zx7w4TDOY9+xDxEvidohbi+8hfR6T53ONlRW/ThK1yW50BQO+BnIylSHNaIPs+Q7uO5rZ3vWDEd8e4hOsmTSObSjfRVe+zG0q/hkeGZMQZ1ZhMC8Kv9E4sbNvN3HDyGE31dKP/Uh8RSDV45Qv5GYvr7+PNvtCuNhC5oLnS90KP3ptfvVhHk5jFcZl72F/50z8T9mmsBZ9RZJ67fTzvldodrIGeleieYzM/1ptChkLbz/qoteBNmTc3+vm7xuNuNT3t7r5t21S/zqfYpKlduz7Pc9GiOnrGNaaNig5vNjOlOiSb0RtymecT0zJKvs9bccaM2ekjekK9lnGHudcz741EyOm2G+fnBmqMuHkEwQ7QU1XdULGSi0Qnh3BLx48bsRn7HBZltYuAVQvVHnCEsBEn/oqp6jKZANog9em2ULm3wKDMmY4ltqtDIxJCUZcLkEx0od1CwOX39CFzI9dGTu4CnAyKY2NM0bZ8Zu9RBhD001U6VOveiHjyoy3fwyj9jefCPqFIPfSOJMdtT24h5Gpl7/xUqUFc6H2NvRrLRdYFvph2s7mtl931+HU9TAVnc66dUI+7raU16Cf4D87/wqmda55ubg9iiN2fmd+tp/xQdGd6Ck/5nGTdojmfvHPwTimqXgIa3Md6qXnlRkx/jTWY+aHyf3SftS/2MVs7qhO6cz+1Z1KCLPjX7X9qCy+RPhWf2E2wfxlXf2JrZcpsq3qU2hQfBbeubXYiLBgnGzs5z4V69yX5XX4NU7al3tdGOeBP03579S4xjsoKTmZPts4v6RL60EvfarrciSfw0DiuXDMtPOc5bKmoWSINm9CI18JP2sDkdvazY7iO7af8pMqc+nL7TauNJ7NL7Qu1M7YSyLkacqpinr0Xs8rOWUaPllQRBtemF+2zaz+TKTHL6KddVI2lwRREu46qMwPsckkhtZulYR8QBud1NVOet7Uyvrhbqf7SA7GS8uxDI/GMepf6vjNtISZ9aHx3Mw61XllMB5h3+pZZ9KzxGniY2Nlk3q+1PTKttcYyRpR6hRPput8flqOPubNy0Y9VGzVA6r/O3mpj7SpWJPnbtBX0wzKJ5CcaWNnATLQxaBqsSX+zQhlgrn2QMa4ajQRuPecMVo7A9fJkHWqk885ArOI6mJJg1pt9IKDMmY3gHmJcUt/JzPjKq/ndW2hjtvKz+PaZF06ydsE1v7SFp9O51LRfKkPPpXmjC6d/nqisx8JtiKFs7/yNZGn8qYhEX81hqlqnsKmJIEGwyk/qOOmeKpgWWxlZGW5NrdflrHZoM1jLZQqR5jIJ44bLggNn8xfbFDnp2IbFkXnENsynyKZwv6NA8lhsG1NtdT5nrSITGWDQT8g2/0r9iP9m67km9lfmXYk96iO4sLALpl3o10XGaE1wKKTYdCv6iY6Rf3COVI+xCE5OK7Z+NF8Y4FPO57aflQWjEkna9fsI9IuiWW9r8pFhSKv4a18rsRq9mmtX6knioKx4cf+I48ylnlZfSrGwoyPROU6JVuxfTzOYTKk1zeIPmw7gwthVXRS+nsKjNWMX9YxChOjh/G1GV3YZ9saIfwNvcowKIgMRlfp1+NdfXqqv/zsgtuUC9XxVfljkcv6+nhkbZmMIaWXzHOx04Q9hS7hGspi+Hn5m12EzrJrxj3kJwSc3aXarvfWfs0nipxFf8PH+F6lagviM9F46qnwbTwbCfbR0H9aHy6NdCx7dSO3DFXyD20mfYOrmf9zfqH0NLJwvd2PmHbDN9siwsl0oxuHu096qQvLH8g9FRdyW5O34xtUbJ6cKbByEJlmWA1RHCV/x6dJIgrVgCSTObpqZ2MQR7xngm3JiEfGIpm6NuKn+LNe6r5ptKTUAsPI0JK1V1zYGdq4EZeI3rBua/lH3ON6wnM8ceIxc7WGppuoHXZmc6spL5y0k76m6cmHD3lzdNI6G05VZ7U4DOzJ9uf5NJovhvLsTaY3Q6vKN0tusw5siy0WZHpLG21oNuM22dv4oO7JMrYNsokl0jawlSajy8SLFor/S29/3HCspnOuy4RNsOidlszaflReP2kbKraZWeuKv2/lf2WOkm5T9i/8wrghfP9b/eB9+V5h9a8hfgvj3CZAH2N+iy8P5+JQj00EnOlreGT7VBxlA6b3IDLnxA765SszrLj5pOIP4a7niPHRFnPqvkHrQB/q/De9uCD/RFAWu/l8PEbT3CLuLsFmkz70uNvW8us1K95LtbWy6K2x3kTOU+4b7ek0S55j4rO6oZTzHJQPvIIOU8lZ2T+zv7wsfFz8IX1M3OR5qnz3VOUsc2gCbz6tpu9SbxA3Nk/OYjuiFggAASAABIAAEAACQAAIAAEgAASOgQCSs2OAh6FAAAgAASAABIAAEAACQAAIAIGTQgDJ2UkhCTpAAAgAASAABIAAEAACQAAIAIFjIIDk7BjgYSgQAAJAAAgAASAABIAAEAACQOCkEEBydlJIgg4QAAJAAAgAASAABIAAEAACQOAYCCA5OwZ4GAoEgAAQAAJAAAgAASAABIAAEDgpBJCcnRSSoAMEgAAQAAJAAAgAASAABIAAEDgGAlslZ/t3jvN7F/T7Evr3JiakN79FMtEPTUBAI+B+A0M3db+HoRtdee63Qlz3k7/Vv2HDv9Ohfo9nQkcWhNvzPCU99G/4zAsa/waMpxvRod9fmeY1QbsSnOhTMJnmQYQmaFQ+Z1iYs5cXhX+nxcfJ/Hsq5vdc/Lip+5Dm1IDTaZv0R/o9qAfBD3IrUZbMy3GfY2Ko5EARCAABIAAEgMBpILBVcpZ/RVs2Dst+xFAvuHM/oFcVHSZny3iaH1U81R+hqxKjcB4QmNgI06ZN++JQXJXcDPsEDd2PWJofAVU/imjq5cMO79dSL4xywsGJyYuDtE8/SDz4gW07xzLdnNB4HiST4zOBH9Od+LHFrL+jJ+LzdT5pGmJYfnTXzOuKo8Sjwiywn8Yk1iPCJv9Qp2Ad8p7Ao6o+gWntowqxfCmlDekoksnGbdPSbjiBc356Zz8NbUL469gajO/mG/eJfYR+pHln4NMi5DjxKj0CGdhu9CPkZc70dozlEZ64AgEgAASAABA4KwS2S87Kr4ev5jYlvJFwizdrNr9B4260yOqFv6KiN5u1Mm8+gv56U6Z6o/hDRWBiA7s0OeMNYN34u82qq9enOMNN9RBr8uVgY8g6+HqVnAk93oi6xCQ6NRpiovln+uON66jdJrx5I+9lEoGn536bq8Ecr/GgyBHM9cqFNuEuPjXa1Et0ieVcakfqZ5KPUWLgfMZiPLJzxsD2HfiiwyKUP/QVQaxcK8b5XhIhi10b09UH43ce7KfdGwO5FS51HrGcHpPGU2RqNapUdQz8TM2BPL9j2ytqKAIBIAAEgAAQOHMEtk7O+k9w7WLIi/bUJ6CyiPOCOb9w0walbYKCjRtBJzQdjN0GorT/49t/ppf199Uf3k03b3+SvnqJMrws3Znv3z5J79z8WfrtZ5ENPk+/vfmzdPPmvfQZ4+Pv2xhn6nyrNmFUIb442uTWTaEQm9kcSrc8B+wmknm5pID602aw+W+lQC0bJGeZTievJkdlo3+el+Mxmn/UV7UTLp1udt5nUSI6ImTUv7Qx7mrDzHo0fP3j1COsR5hGcSDe6EfyR3UjewR9jU2yvsQ7tEvQV9Bbeg2x8fhGxKiPSvQEnwg7Gt7VB+MlOQt1ZRl6vMbzJWPe+6H4ffOX7AcNY5LVyOBkjeBAHRAAAkAACACBs0Zg++Ssk/QgHbzISRNvgtUC33VdWjFcPDMfs9ASzUH/bgNR+Nfk5LN7KhFoG//afgoJFJKzUXL2dXp4+2fpnT983SXOEWbGlXhT6xN9vVnzSVK/KZQNXbj5M8yizWDZrFICQ76oTgXCMs+Rlvywn86NGbY3PXlDXedfpKNWpPGX0yQ7r6RdrnoslTP9OPH0fRf2D+3o7Sr3TW/hlnFUSZ40sE2CemmXa5gckZ6e1wiTEov0h1OOJttotU7rJ/vCtV4j+4X+w77gZcpkGAOfSE/4ZLW5i6Esy6aPNVbf8/Otqnisgsg0JkJ2Ef+Yv1bdhwSzj+ukddgVDUAACAABIAAEjonAiSRneaMxswiWjYLuWxdF2rj4jQQp5jYKTdfNFt9RsliTLyRnXSKUscmJ0s2b76aHfzvhpHV0cka2GJ4oZnn0aVvzCVVyG2HV4k6wfOJSNmFTGzu18XwZJ2e06Z5OhMrcqHJ6HTUaVNYJRtS3tD+gU7N1Wle6QqeNscllToL0fB8nGBQ7VJIxYT/hmq9admkp+q+CJIyTk520Ez1ip/QimXuMA15zcur4pfvqehG7Xov8VZ6Gb+1SC4FMpW2cnAW4VHotqTS2kuSsytQGMB9dzxjbtYCxZP1tvebBfczY7A/Wp8bjiVZdT4xPN1n70hS2unfuh+RMY4IyEAACQAAInBYCGydnerMli6HfzPiNgb+XT9tlfN7k6sW1qDvcxOQNTB0v6Az6dxuI0p9PYvjxOXqETv3p5IATN2nTSYo8akdtVN/uW/IgyU0Zr+jWUyBFv42bToTmxzZZSK/oFKompt2poB2rEyWD173PU70XvZQuPV+Nxbvp4WfRyVmffHk5q+5FbjG9ueqNsGnwmzF3z5vDddrn8SpZEBrev4J+zdfLJnsi0cv+O9hgB7RJjEZfhKLxbcNd52fdMDsdZVi9av5RX90ePVIWjBnizxrw94/65KcKVB7LnN6It429tVOe6ztphzEh2QM60QdBwp59wI5hOwU69bYQIsE1GB/0ao/gOvs1fa1sJqlVBEPZxL9Vv64oPu7kzbjuJv8exa5exsu1Y7CkwvqcH8E+PmVDTs48TuP7bh3xDHEPBIAAEAACQOAMEdg4Ocuy2Q1Z3RBGGyGpM4upHc80o8U8quPOedPVLaqD/t0GogBcN/6cVMj3m1RixPUqIfP3lCDwCdC76bf3Pinfj5LxJRm593k5lbL3Ocl4N71T2j+7RwlcIEOXPP0zJ0W3R2NzctUSMn8v8sVXlqPKHI/Nfe6lh+bRQ+qrsHInYzmRk/aWqNmE1NEIdM94N5yKKe3FbSxbo/c7f1968ni76ecW7190r098wuQp0/QfYDSZBhtRlsFuKOvpQt24l+Tjzm46eKEes6RTrtpnoGMVQPPPfftEQGOR+7TkKpiLQ/yJqR9fBWmFyfGtmz31E/0luW4JaxsRyNoayylixjzHFoVdYA+DE8W3uT4SC6Mr2avovUsvM6n2MwIuvtk6ORMOzgZML5Kb6iJZ/VwRuouu2if7AcuSM+2zPY1co+w76oJ6IAAEgAAQAAJnjMCJJWdts9Z/ut9vFKJFMdi0DRf4weI96L9tcmYTFUpmgmSlJCEtGSpJj0tOaiJYEo6crLQk4x9R4hclJ9+W5EwncnoslxXdb/+ZWA853RrQzPLlpKnp4u+zbkxP8w9paqxsYsq8Iny4ThK4OHmUZFgeswzni9pYTm4q9WZTbzCnNtm6HydnNgkQX1/+gYXyZaanE7Jggym6iYz6Qw/5jSgzD6K5plFT/EviZD/00O1lHMspslG7O/UWGTWbWg7meW0rBdFN22dYFjnyI3ks+5D/DG/Six7drPrMYZflnU0WtD7aXl7vJ/QdtPaSjfFr37WPSDn2Q8OC7Wb7mfby4QLHci2zvIKefN9h62Mr3dcPEYrNdu7k1+ObZDawZ/O7wOeUoLN44+RMoYUiEAACQAAIvGoInFhyNrfw2hcsDDY9tPD7za++F3T1xiFY5ENZAjo1YQoSmn98GyQUpa4lL+3kTJKFSjNKPlQS4x/P2zg508mWSs66pE+SOd1fyVHlLXU2Ic0Jlj3dKslePV1rSVTmLY+A5mvGKsAywucUkjNxGb7y5nQVvHHQ9ConIGrT75rlljeJzq8kOZM+cqW+8QcYg40o+3gkQ5475OOanvDhK+lZ5RrMtTpA84/66vY6SH13L2h3G/g2ikqZx1B26jI5XlMLeM+M98mEppbLRFOSzQgPP2JGH9FFrpJAezLqXmTk5GwqmZMxQlvuRye4GydnLZETmQ6CBF4nS9SvJmfVB5VgXJzDdWDXQkbz85Tz/fT4NmZOjtYTJSAABIAAEAACZ4XAiSVnerPFC7naVPh72aC1T0pjdduGwLWPNhlmU9rGjOjUxCRMzqIkRJ8G6ROy4LQnSj5UUnRayVlO8rY9OdMnYzq5agkYYWYTOI2DfjW+xmphcsYnkwGWCrfljzXKiYIkOG3TTZu7Sd/jza6Ma35U3+RYPxAofdTmuPf1PN4nZ+1+sJEcyMAbU+Kv5lf3YhIzD+Y2oJp/1Fe3ayykHLQrPKRXu2YeOl60tlLi8WK/uWtgpyn+HDuCMVUI0kf8Q/DIddGHPvKa+FAfHaeUTCMfERFsvMoyRLylLvLlkIeWR5i5K41jXZS81MXIVOjw45fuQ4I6nvqY5EzbXXDN32Hs5Q98SsnJc0D7v2rLxbG9BDN97fl3BFEBBIAAEAACQODMEDh3yRlvAurmVzZJFg9enM3CX9q7DUGuNxsLRWouOetOs9QJVR07PO3pExJKauTUbVFyxvx+1r29cHqsTooocfL3NtGqenAClGX2J2W2z8LkrCSnRl/9nbSim+U1z9/rrsypXl/fPvHP7Xmz1jbQ+X64KeON6dQG3nA1bxVlXws2jjkZ0z/GK/QHG1EvA2+IKVGR71TJeHnDntLZzIO2EXZSl1vNP+qr2wMKXk7qYjb2RFPJtuTkrLIZ8Y7krIMcf1XPxTy2+YLIK3gST4k7M3xG9Mrv2rGthL3BpCQ76kUu0o2uo3iV+yyRqdDwfsg+pG2huRbqS5Iz0S+IwSQ7Y2t80Puo0sHhkqWwdve/bzefnIleio9UlWuej/71Jq5Tvc10bLJZG1EAAkAACAABIHCiCGyXnPGC2h6r8gtd3qDu8lvZ5BNKvRHmdv/p/1K1Cm9Nrw71G4LSkOXpf0+oJR05galvbNSPAEqCxG9z1Kc6boy87dE87lcSNGm7/Un67G/597t8ktElgpQsCW8tT/SYIvcbyyYJUtN3nKCxXCKvXAv/sE0lXKb99ifpIb/kpJ2m5e+qlcce6YUm0Y9Qky5O3yZ3n7xV2w8K4mtmM859pzZcdnM4IF2r9WZx5Gt+jtTBo9d+101rkdNt5LNeeaPd8TTzYLxBzTJoXYWXP62SxKVJLSUth9TV5IyTAf/CiMyjt4ckSZ730nslY8WuSmQLLJfqz/eStOTkTOIWXcNYIxR9PCr35mST+kYyDfoypkHik1nO2bP0opeKHDs5K9jr75zV5Lp80OB4kOw1OSs+S79/uXujrRf+yYle3+KTT3bTDn9QJ7bJuun5lmvk/9522o5z5bGdy7wY2kT44woEgAAQAAJA4PgIbJ6clQ0X/XgqfcIcbrIm5MqbOdoYyUbQLrwTQ7mJx7sNQR1DspUFNPNpG7to4W2b/nGycrH6UMJpH4mUkzd7wnWaeOUELEoou4T2239W00cF3sS5pKbrV/zZ+7H3n+mNXfPhzcaJf7ZEIctc6kd+LkoU2bsEQs0DvxGWofXKCYLwjzb+ZaNMb4OUUx11st3xpk5VLqGbx+b/Mw+Pt+5Ry0ynYVvrg+89tbZBImQ6lJ8EKG/atJv9HNdyvIjw0Pq15IXPYFjeSOdpmbyfsg8NEwEtn1NKkj1nn2nfVT7435IM+YRaTvpy32a7EsNF1mp3eey2rBE3/NsnPa50r3BTekRx29rLYaBvjW/rhtP5cWzLAXdAAAgAASAABLZDYOPkjBZGvWDmjYUs8DPX8mOmevxGm9m5zeqGGFysxCsnVOb0Sk7G5LfQokc0Z747dzoYyqmkJIr+viWHG5r81LuzP2/kpzb5OREBaZMsG+Ygkenm3Ebyzks4vXnOG/O2wff0yoZ/8mTdb+4dDd6UR0md7ddwUImB7XJydwtlIoYsV7VfFqHJSjF2XreTE5wlcidflnqWbV6mpTpE+muO0/4liXefYHoaYx/UPVEGAkAACAABIHC2CGycnJ2teKfL7XQSi5Y4vIr0o+QtOsU6L7qdroeAOhAAAkAACAABIAAEgAAQODsELnRydnYwgxMQAAJAAAgAASAABIAAEAACQGAaASRn0/igFQgAASAABIAAEAACQAAIAAEgcCYIIDk7E5jBBAgAASAABIAAEAACQAAIAAEgMI0AkrNpfNAKBIAAEAACQAAIAAEgAASAABA4EwSQnJ0JzGACBIAAEAACQAAIAAEgAASAABCYRgDJ2TQ+aAUCQAAIAAEgAASAABAAAkAACJwJAkjOzgRmMAECQAAIAAEgAASAABAAAkAACEwjgORsGh+0AgEgAASAABAAAkAACAABIAAEzgQBJGdnAjOYAAEgAASAABAAAkAACAABIAAEphFAcjaND1qBABAAAkAACAABIAAEgAAQAAJnggCSszOBGUyAABAAAkAACAABIAAEgAAQAALTCCA5m8YHrUAACAABIAAEgAAQAAJAAAgAgTNBAMnZmcAMJkAACAABIABjAiyXAAAAfUlEQVQEgAAQAAJAAAgAgWkEkJxN44NWIAAEgAAQAAJAAAgAASAABIDAmSCA5OxMYAYTIAAEgAAQAAJAAAgAASAABIDANAJIzqbxQSsQAAJAAAgAASAABIAAEAACQOBMEEBydiYwgwkQAAJAAAgAASAABIAAEAACQGAagf8Hhv69hE6J3v0AAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Disabling Gradient Tracking\n",
    "---------------------------\n",
    "\n",
    "By default, all tensors with ``requires_grad=True`` are tracking their\n",
    "computational history and support gradient computation. However, there\n",
    "are some cases when we do not need to do that, for example, when we have\n",
    "trained the model and just want to apply it to some input data, i.e. we\n",
    "only want to do *forward* computations through the network. We can stop\n",
    "tracking computations by surrounding our computation code with\n",
    "``torch.no_grad()`` block:\n",
    "\n",
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "z = torch.matmul(x, w)+b\n",
    "print(z.requires_grad)\n",
    "\n",
    "with torch.no_grad():\n",
    "    z = torch.matmul(x, w)+b\n",
    "print(z.requires_grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to achieve the same result is to use the ``detach()`` method\n",
    "on the tensor:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 实现相同结果的另一种detach()方法是在张量上使用该方法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "z = torch.matmul(x, w)+b\n",
    "z_det = z.detach()\n",
    "print(z_det.requires_grad) "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are reasons you might want to disable gradient tracking:\n",
    "  - To mark some parameters in your neural network at **frozen parameters**. This is\n",
    "    a very common scenario for\n",
    "    `finetuning a pretrained network <https://pytorch.org/tutorials/beginner/finetuning_torchvision_models_tutorial.html>`__\n",
    "  - To **speed up computations** when you are only doing forward pass, because computations on tensors that do\n",
    "    not track gradients would be more efficient.\n",
    " ![image.png](attachment:image.png)\n"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More on Computational Graphs\n",
    "----------------------------\n",
    "Conceptually, autograd keeps a record of data (tensors) and all executed\n",
    "operations (along with the resulting new tensors) in a directed acyclic\n",
    "graph (DAG) consisting of\n",
    "`Function <https://pytorch.org/docs/stable/autograd.html#torch.autograd.Function>`__\n",
    "objects. In this DAG, leaves are the input tensors, roots are the output\n",
    "tensors. By tracing this graph from roots to leaves, you can\n",
    "automatically compute the gradients using the chain rule.\n",
    "\n",
    "In a forward pass, autograd does two things simultaneously:\n",
    "\n",
    "- run the requested operation to compute a resulting tensor\n",
    "- maintain the operation’s *gradient function* in the DAG.\n",
    "\n",
    "The backward pass kicks off when ``.backward()`` is called on the DAG\n",
    "root. ``autograd`` then:\n",
    "\n",
    "- computes the gradients from each ``.grad_fn``,\n",
    "- accumulates them in the respective tensor’s ``.grad`` attribute\n",
    "- using the chain rule, propagates all the way to the leaf tensors.\n",
    "\n",
    "\n",
    "  \n",
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-8-b8ed9f8582e0>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-8-b8ed9f8582e0>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    <div class=\"alert alert-info\"><h4>Note</h4><p>**DAGs are dynamic in PyTorch**\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\"><h4>Note</h4><p>**DAGs are dynamic in PyTorch**\n",
    "  An important thing to note is that the graph is recreated from scratch; after each\n",
    "  ``.backward()`` call, autograd starts populating a new graph. This is\n",
    "  exactly what allows you to use control flow statements in your model;\n",
    "  you can change the shape, size and operations at every iteration if\n",
    "  needed.</p></div>\n",
    "\n",
    "Optional Reading: Tensor Gradients and Jacobian Products\n",
    "--------------------------------------\n",
    "\n",
    "In many cases, we have a scalar loss function, and we need to compute\n",
    "the gradient with respect to some parameters. However, there are cases\n",
    "when the output function is an arbitrary tensor. In this case, PyTorch\n",
    "allows you to compute so-called **Jacobian product**, and not the actual\n",
    "gradient.\n",
    "\n",
    "For a vector function $\\vec{y}=f(\\vec{x})$, where\n",
    "$\\vec{x}=\\langle x_1,\\dots,x_n\\rangle$ and\n",
    "$\\vec{y}=\\langle y_1,\\dots,y_m\\rangle$, a gradient of\n",
    "$\\vec{y}$ with respect to $\\vec{x}$ is given by **Jacobian\n",
    "matrix**:\n",
    "\n",
    "\\begin{align}J=\\left(\\begin{array}{ccc}\n",
    "      \\frac{\\partial y_{1}}{\\partial x_{1}} & \\cdots & \\frac{\\partial y_{1}}{\\partial x_{n}}\\\\\n",
    "      \\vdots & \\ddots & \\vdots\\\\\n",
    "      \\frac{\\partial y_{m}}{\\partial x_{1}} & \\cdots & \\frac{\\partial y_{m}}{\\partial x_{n}}\n",
    "      \\end{array}\\right)\\end{align}\n",
    "\n",
    "Instead of computing the Jacobian matrix itself, PyTorch allows you to\n",
    "compute **Jacobian Product** $v^T\\cdot J$ for a given input vector\n",
    "$v=(v_1 \\dots v_m)$. This is achieved by calling ``backward`` with\n",
    "$v$ as an argument. The size of $v$ should be the same as\n",
    "the size of the original tensor, with respect to which we want to\n",
    "compute the product:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First call\n",
      " tensor([[4., 2., 2., 2., 2.],\n",
      "        [2., 4., 2., 2., 2.],\n",
      "        [2., 2., 4., 2., 2.],\n",
      "        [2., 2., 2., 4., 2.],\n",
      "        [2., 2., 2., 2., 4.]])\n",
      "\n",
      "Second call\n",
      " tensor([[8., 4., 4., 4., 4.],\n",
      "        [4., 8., 4., 4., 4.],\n",
      "        [4., 4., 8., 4., 4.],\n",
      "        [4., 4., 4., 8., 4.],\n",
      "        [4., 4., 4., 4., 8.]])\n",
      "\n",
      "Call after zeroing gradients\n",
      " tensor([[4., 2., 2., 2., 2.],\n",
      "        [2., 4., 2., 2., 2.],\n",
      "        [2., 2., 4., 2., 2.],\n",
      "        [2., 2., 2., 4., 2.],\n",
      "        [2., 2., 2., 2., 4.]])\n"
     ]
    }
   ],
   "source": [
    "inp = torch.eye(5, requires_grad=True)\n",
    "out = (inp+1).pow(2)\n",
    "out.backward(torch.ones_like(inp), retain_graph=True)\n",
    "print(\"First call\\n\", inp.grad)\n",
    "out.backward(torch.ones_like(inp), retain_graph=True)\n",
    "print(\"\\nSecond call\\n\", inp.grad)\n",
    "inp.grad.zero_()\n",
    "out.backward(torch.ones_like(inp), retain_graph=True)\n",
    "print(\"\\nCall after zeroing gradients\\n\", inp.grad)"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that when we call ``backward`` for the second time with the same\n",
    "argument, the value of the gradient is different. This happens because\n",
    "when doing ``backward`` propagation, PyTorch **accumulates the\n",
    "gradients**, i.e. the value of computed gradients is added to the\n",
    "``grad`` property of all leaf nodes of computational graph. If you want\n",
    "to compute the proper gradients, you need to zero out the ``grad``\n",
    "property before. In real-life training an *optimizer* helps us to do\n",
    "this.\n",
    "\n",
    " ![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-info\"><h4>Note</h4><p>Previously we were calling ``backward()`` function without\n",
    "          parameters. This is essentially equivalent to calling\n",
    "          ``backward(torch.tensor(1.0))``, which is a useful way to compute the\n",
    "          gradients in case of a scalar-valued function, such as loss during\n",
    "          neural network training.</p></div>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Further Reading\n",
    "~~~~~~~~~~~~~~~~~\n",
    "- `Autograd Mechanics <https://pytorch.org/docs/stable/notes/autograd.html>`_\n",
    "\n"
   ]
  }
 ],
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